This was supposed to be Tim Pigott-Smith's Salesman. Announced with appropriate fanfare back in the spring, rehearsals were well under way when the distinguished actor died suddenly and unexpectedly. It's appropriate that the rescheduled tour is dedicated to his memory.

Stepping into the role of Willy Loman, Arthur Miller's complex and tragic creation, was never going to be an easy task. Nicholas Woodeson, a safe pairs of hands as well as an actor of great sensitivity and subtlety, takes on the job with humility and considerable class.

If there's an undercurrent of trepidation about his performance, one can only imagine that it's partly due to the shadow of sadness across the whole production. But Woodeson intelligently mines this seam to give Willy a tangible sense of vacillation, lurching from insane pride in his sons Biff and Happy to outbursts of rage at their failure to live up to his aspirations.

Ultimately, of course, the failure is Willy's – the gradual collapse of his optimism and belief in the illusory American Dream is the story of Miller's play – and Woodeson makes it painfully believable. At his side is a quietly supportive wife Linda, played with simple sincerity by Tricia Kelly, another late replacement for Pigott-Smith's wife Pamela Miles.

Much of Willy's disintegration in Miller's script depends on his relationship with the boys. Here, fortunately, Biff and Happy are terrific. Ben Deery's Happy – probably the trickier of the two roles – emerges as a would-be replica of his father, willing to deceive himself as much as the rest of the world about how well he's doing and how bright his future is. George Taylor as Biff brings a youthful turmoil to the conflicted boy, desperate to retain faith in a parent who is transparently not the man he thought he was. The interplay between the two of them and Willy is crucial to the dynamic of the production.

There's a supporting cast of strong players, from Thom Tuck's weaselly boss Howard to Geff Francis's touching performance as next-door neighbor Charley. Less successful, perhaps, is Georgia Lowe's design, which places the action in a minimalist grey box of a set, with panels of light denoting different spaces. Emblazoned with the stuttering neon legend ‘Land of the Free', the message is not so much subliminal as stark.

There are some strange directorial choices too, such as a host of anachronisms among the furniture and props. So a beaten-up 1940s refrigerator has a cordless telephone hanging from it, while shiny-suited 1980s business types socialise in a thoroughly modern New York eaterie. If director Abigail Graham is working in metaphor here, I'm afraid it was lost on me.

But it's a sound, solid production of Miller's masterpiece and certainly goes down well with the teenagers in the audience for whom it is on the A-level syllabus. It's also a worthy tribute to the man who was to have been Willy Loman.

Death of a Salesman runs at Royal & Derngate until 17 June and then tours to King's Theatre, Edinburgh, Hall for Cornwall, Truro, Yvonne Arnaud Theatre, Guildford and Oxford Playhouse.